12n
0348
(K12n
0348
)
A knot diagram
1
Linearized knot diagam
3 5 8 12 2 11 3 4 5 7 10 9
Solving Sequence
4,12 5,8
9 10 1 3 2 6 7 11
c
4
c
8
c
9
c
12
c
3
c
2
c
5
c
7
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.60524 × 10
82
u
54
+ 4.32163 × 10
82
u
53
+ ··· + 2.31107 × 10
83
b + 9.23794 × 10
83
,
− 5.24600 × 10
82
u
54
− 1.43004 × 10
83
u
53
+ ··· + 2.31107 × 10
83
a + 3.49791 × 10
83
,
u
55
+ 3u
54
+ ··· − 12u − 11i
I
u
2
= hu
15
− u
14
+ ··· + b + 5, 10u
15
− 26u
14
+ ··· + a − 13, u
16
− 2u
15
+ ··· + 8u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 71 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h2.61 × 10
82
u
54
+ 4.32 × 10
82
u
53
+ · · · + 2.31 × 10
83
b + 9.24 ×
10
83
, −5.25 × 10
82
u
54
− 1.43 × 10
83
u
53
+ · · · + 2.31 × 10
83
a + 3.50 ×
10
83
, u
55
+ 3u
54
+ · · · − 12u − 11i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
0.226994u
54
+ 0.618778u
53
+ ··· − 10.4791u − 1.51354
−0.112728u
54
− 0.186996u
53
+ ··· − 4.08158u − 3.99725
a
9
=
0.114266u
54
+ 0.431782u
53
+ ··· − 14.5607u − 5.51080
−0.112728u
54
− 0.186996u
53
+ ··· − 4.08158u − 3.99725
a
10
=
0.107387u
54
+ 0.305810u
53
+ ··· − 8.15437u − 0.534709
−0.0799915u
54
− 0.0948860u
53
+ ··· − 5.42127u − 5.15595
a
1
=
0.908704u
54
+ 3.08911u
53
+ ··· − 23.8651u − 16.2385
−0.447095u
54
− 1.15334u
53
+ ··· + 7.94778u − 2.70823
a
3
=
−0.172479u
54
− 1.13662u
53
+ ··· + 24.4494u + 14.6350
−0.0737233u
54
− 0.0490777u
53
+ ··· + 2.74375u − 3.73277
a
2
=
0.0660274u
54
− 0.351978u
53
+ ··· + 12.3782u + 11.5567
−0.207205u
54
− 0.434267u
53
+ ··· + 6.19685u − 2.97237
a
6
=
0.0217548u
54
− 0.00585046u
53
+ ··· − 3.61926u − 1.19908
0.340641u
54
+ 0.992765u
53
+ ··· − 11.1110u + 1.49013
a
7
=
0.281862u
54
+ 1.12478u
53
+ ··· − 14.1050u − 9.98072
−0.0168458u
54
− 0.208276u
53
+ ··· + 6.42777u + 1.43253
a
11
=
0.520294u
54
+ 1.83552u
53
+ ··· − 15.1557u − 6.44576
−0.335273u
54
− 1.03983u
53
+ ··· + 8.71346u − 0.0705450
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.313768u
54
− 0.790410u
53
+ ··· + 2.10169u − 8.23967
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 63u
54
+ ··· − 20918u − 169
c
2
, c
5
u
55
+ u
54
+ ··· + 86u − 13
c
3
, c
7
, c
8
u
55
+ u
54
+ ··· + 22u
2
− 23
c
4
u
55
+ 3u
54
+ ··· − 12u − 11
c
6
, c
10
u
55
− 3u
54
+ ··· + 84u − 17
c
9
u
55
− u
54
+ ··· − 325045u − 237989
c
11
u
55
+ 37u
54
+ ··· − 1784u − 289
c
12
u
55
+ 11u
54
+ ··· + 89882u + 16337
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− 137y
54
+ ··· + 108847246y −28561
c
2
, c
5
y
55
+ 63y
54
+ ··· − 20918y −169
c
3
, c
7
, c
8
y
55
− 43y
54
+ ··· + 1012y −529
c
4
y
55
+ 21y
54
+ ··· − 4740y −121
c
6
, c
10
y
55
+ 37y
54
+ ··· − 1784y −289
c
9
y
55
− 23y
54
+ ··· − 63034731065y −56638764121
c
11
y
55
− 27y
54
+ ··· − 78420y −83521
c
12
y
55
− 3y
54
+ ··· + 4960988170y −266897569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.815485 + 0.609992I
a = 0.716376 − 0.340161I
b = −1.240990 + 0.607346I
−3.46247 − 2.90307I 4.19084 + 1.32778I
u = −0.815485 − 0.609992I
a = 0.716376 + 0.340161I
b = −1.240990 − 0.607346I
−3.46247 + 2.90307I 4.19084 − 1.32778I
u = −0.766697 + 0.587191I
a = 0.121340 − 0.656968I
b = −0.288763 − 0.617191I
−3.36899 + 1.08421I −1.34816 − 2.39352I
u = −0.766697 − 0.587191I
a = 0.121340 + 0.656968I
b = −0.288763 + 0.617191I
−3.36899 − 1.08421I −1.34816 + 2.39352I
u = −0.342407 + 0.888408I
a = −0.352056 + 0.222676I
b = 0.093000 + 0.425608I
0.55048 + 1.48371I 4.97976 − 5.81830I
u = −0.342407 − 0.888408I
a = −0.352056 − 0.222676I
b = 0.093000 − 0.425608I
0.55048 − 1.48371I 4.97976 + 5.81830I
u = −0.181810 + 1.053110I
a = −0.138751 + 0.733731I
b = 0.759862 + 0.688944I
−3.21509 + 2.62066I 1.87813 − 3.80550I
u = −0.181810 − 1.053110I
a = −0.138751 − 0.733731I
b = 0.759862 − 0.688944I
−3.21509 − 2.62066I 1.87813 + 3.80550I
u = −0.722892 + 0.803711I
a = 2.14118 − 1.56678I
b = −1.38166 − 0.45730I
−7.22887 + 2.83374I 2.38389 − 3.49922I
u = −0.722892 − 0.803711I
a = 2.14118 + 1.56678I
b = −1.38166 + 0.45730I
−7.22887 − 2.83374I 2.38389 + 3.49922I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173002 + 0.887529I
a = 2.29349 + 0.99676I
b = −1.53634 + 0.17332I
7.27746 − 3.45379I 10.27416 + 1.32847I
u = 0.173002 − 0.887529I
a = 2.29349 − 0.99676I
b = −1.53634 − 0.17332I
7.27746 + 3.45379I 10.27416 − 1.32847I
u = 0.628360 + 0.597283I
a = 1.092470 − 0.206282I
b = −0.537582 − 0.337146I
−0.59371 − 3.25938I 2.97394 − 0.66796I
u = 0.628360 − 0.597283I
a = 1.092470 + 0.206282I
b = −0.537582 + 0.337146I
−0.59371 + 3.25938I 2.97394 + 0.66796I
u = −0.711127 + 0.948848I
a = −0.966349 + 0.247086I
b = 1.34857 − 0.64792I
−6.77729 + 2.66101I 0
u = −0.711127 − 0.948848I
a = −0.966349 − 0.247086I
b = 1.34857 + 0.64792I
−6.77729 − 2.66101I 0
u = 0.800334 + 0.884723I
a = 0.677563 − 0.092095I
b = −0.119062 + 1.076690I
−6.90102 − 2.99599I 0
u = 0.800334 − 0.884723I
a = 0.677563 + 0.092095I
b = −0.119062 − 1.076690I
−6.90102 + 2.99599I 0
u = −0.598983 + 1.067040I
a = 0.455882 − 0.093492I
b = 0.309654 − 0.497235I
−1.80177 + 4.16956I 0
u = −0.598983 − 1.067040I
a = 0.455882 + 0.093492I
b = 0.309654 + 0.497235I
−1.80177 − 4.16956I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.992759 + 0.740017I
a = −0.766608 − 0.114418I
b = 0.059829 − 0.980635I
−11.75940 + 2.31711I 0
u = 0.992759 − 0.740017I
a = −0.766608 + 0.114418I
b = 0.059829 + 0.980635I
−11.75940 − 2.31711I 0
u = 0.682830 + 0.316170I
a = 0.666716 − 0.682016I
b = −0.911518 − 0.401923I
−1.67294 + 2.77507I 2.05247 − 3.78121I
u = 0.682830 − 0.316170I
a = 0.666716 + 0.682016I
b = −0.911518 + 0.401923I
−1.67294 − 2.77507I 2.05247 + 3.78121I
u = −0.648251 + 1.072510I
a = −0.698611 + 0.921968I
b = 0.946204 + 0.085319I
1.85295 + 1.10015I 0
u = −0.648251 − 1.072510I
a = −0.698611 − 0.921968I
b = 0.946204 − 0.085319I
1.85295 − 1.10015I 0
u = 0.577460 + 1.116900I
a = −1.83686 − 1.43049I
b = 1.113190 − 0.366716I
0.58204 − 7.69168I 0
u = 0.577460 − 1.116900I
a = −1.83686 + 1.43049I
b = 1.113190 + 0.366716I
0.58204 + 7.69168I 0
u = 0.461578 + 1.175220I
a = 1.85272 + 0.82840I
b = −1.234160 + 0.257600I
4.47795 − 4.19285I 0
u = 0.461578 − 1.175220I
a = 1.85272 − 0.82840I
b = −1.234160 − 0.257600I
4.47795 + 4.19285I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264238 + 0.685778I
a = 0.53501 − 4.66877I
b = −0.937038 + 0.123287I
−4.80330 − 0.56532I 4.34221 − 3.19087I
u = −0.264238 − 0.685778I
a = 0.53501 + 4.66877I
b = −0.937038 − 0.123287I
−4.80330 + 0.56532I 4.34221 + 3.19087I
u = −0.712473 + 1.066430I
a = −1.88688 + 1.00057I
b = 1.41881 + 0.51710I
−2.09404 + 8.67779I 0
u = −0.712473 − 1.066430I
a = −1.88688 − 1.00057I
b = 1.41881 − 0.51710I
−2.09404 − 8.67779I 0
u = −0.004077 + 0.715907I
a = −3.38106 − 1.04947I
b = 1.53871 + 0.03923I
6.53124 + 2.75926I 7.77095 − 4.45417I
u = −0.004077 − 0.715907I
a = −3.38106 + 1.04947I
b = 1.53871 − 0.03923I
6.53124 − 2.75926I 7.77095 + 4.45417I
u = 0.119783 + 0.703838I
a = −0.805794 + 0.305998I
b = 0.362409 + 0.453693I
1.003320 + 0.902305I 8.30926 − 5.19000I
u = 0.119783 − 0.703838I
a = −0.805794 − 0.305998I
b = 0.362409 − 0.453693I
1.003320 − 0.902305I 8.30926 + 5.19000I
u = 0.995644 + 0.888830I
a = −1.031330 − 0.818819I
b = 1.356040 − 0.197721I
1.77258 − 3.90284I 0
u = 0.995644 − 0.888830I
a = −1.031330 + 0.818819I
b = 1.356040 + 0.197721I
1.77258 + 3.90284I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.126954 + 1.333810I
a = −1.95011 + 0.22052I
b = 1.128790 − 0.066319I
3.06772 − 0.82361I 0
u = 0.126954 − 1.333810I
a = −1.95011 − 0.22052I
b = 1.128790 + 0.066319I
3.06772 + 0.82361I 0
u = 0.813384 + 1.075410I
a = −0.501571 + 0.076047I
b = 0.070094 − 1.130120I
−10.66830 − 8.91439I 0
u = 0.813384 − 1.075410I
a = −0.501571 − 0.076047I
b = 0.070094 + 1.130120I
−10.66830 + 8.91439I 0
u = 0.650155
a = −0.555963
b = 0.901498
1.30158 8.19850
u = −1.222360 + 0.639856I
a = −0.680782 + 0.122900I
b = 1.288840 − 0.499125I
−7.94459 − 7.58411I 0
u = −1.222360 − 0.639856I
a = −0.680782 − 0.122900I
b = 1.288840 + 0.499125I
−7.94459 + 7.58411I 0
u = −1.035520 + 0.922159I
a = 0.550770 − 0.481659I
b = −0.990991 − 0.201391I
0.50650 + 5.61395I 0
u = −1.035520 − 0.922159I
a = 0.550770 + 0.481659I
b = −0.990991 + 0.201391I
0.50650 − 5.61395I 0
u = −0.82989 + 1.20266I
a = 1.60979 − 0.92855I
b = −1.40604 − 0.54304I
−6.0591 + 14.8324I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.82989 − 1.20266I
a = 1.60979 + 0.92855I
b = −1.40604 + 0.54304I
−6.0591 − 14.8324I 0
u = 0.69303 + 1.48402I
a = 1.37520 + 0.37724I
b = −1.330370 + 0.097750I
3.52220 − 3.74412I 0
u = 0.69303 − 1.48402I
a = 1.37520 − 0.37724I
b = −1.330370 − 0.097750I
3.52220 + 3.74412I 0
u = −0.033996 + 0.282179I
a = −0.63193 − 1.74588I
b = −0.830222 − 0.601183I
−1.96989 + 2.37563I −2.00410 − 0.86695I
u = −0.033996 − 0.282179I
a = −0.63193 + 1.74588I
b = −0.830222 + 0.601183I
−1.96989 − 2.37563I −2.00410 + 0.86695I
10
II.
I
u
2
= hu
15
−u
14
+· · ·+b+5, 10u
15
−26u
14
+· · ·+a−13, u
16
−2u
15
+· · ·+8u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
−10u
15
+ 26u
14
+ ··· − 32u + 13
−u
15
+ u
14
+ ··· − 6u − 5
a
9
=
−11u
15
+ 27u
14
+ ··· − 38u + 8
−u
15
+ u
14
+ ··· − 6u − 5
a
10
=
−6u
15
+ 16u
14
+ ··· − 21u + 8
−2u
15
+ 4u
14
+ ··· − 11u − 4
a
1
=
−26u
15
+ 57u
14
+ ··· − 103u + 12
−u
15
+ u
14
+ ··· − 5u − 7
a
3
=
6u
15
− 13u
14
+ ··· + 31u − 6
u
15
− 2u
14
+ ··· + 2u + 1
a
2
=
5u
15
− 11u
14
+ ··· + 23u − 6
u
15
− 2u
14
+ ··· + 3u + 1
a
6
=
6u
15
− 7u
14
+ ··· + 20u + 24
−u
15
+ 3u
14
+ ··· − 8u + 3
a
7
=
−2u
15
− 8u
13
+ ··· − 10u − 10
−3u
15
+ 6u
14
+ ··· + 2u − 1
a
11
=
−13u
15
+ 30u
14
+ ··· − 46u + 14
−2u
15
+ 5u
14
+ ··· − 11u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −13u
15
+ 19u
14
− 69u
13
+ 42u
12
− 161u
11
+ 50u
10
− 278u
9
−
24u
8
− 320u
7
− 121u
6
− 269u
5
− 156u
4
− 127u
3
− 89u
2
− 34u − 13
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 16u
15
+ ··· − 10u + 1
c
2
u
16
+ 8u
14
+ ··· − 2u + 1
c
3
u
16
− 9u
14
+ ··· − 2u + 1
c
4
u
16
− 2u
15
+ ··· + 8u
2
+ 1
c
5
u
16
+ 8u
14
+ ··· + 2u + 1
c
6
u
16
− 2u
15
+ ··· + 6u
2
+ 1
c
7
, c
8
u
16
− 9u
14
+ ··· + 2u + 1
c
9
u
16
+ 5u
14
+ ··· − u + 1
c
10
u
16
+ 2u
15
+ ··· + 6u
2
+ 1
c
11
u
16
+ 10u
15
+ ··· + 12u + 1
c
12
u
16
+ 4u
15
+ ··· − 4u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 28y
15
+ ··· + 14y + 1
c
2
, c
5
y
16
+ 16y
15
+ ··· + 10y + 1
c
3
, c
7
, c
8
y
16
− 18y
15
+ ··· − 8y + 1
c
4
y
16
+ 10y
15
+ ··· + 16y + 1
c
6
, c
10
y
16
+ 10y
15
+ ··· + 12y + 1
c
9
y
16
+ 10y
15
+ ··· − 3y + 1
c
11
y
16
+ 2y
15
+ ··· + 116y
2
+ 1
c
12
y
16
− 18y
15
+ ··· − 18y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.350363 + 0.993044I
a = 2.25243 + 0.60422I
b = −1.57289 + 0.06836I
7.04961 − 4.51747I 8.24086 + 7.83910I
u = 0.350363 − 0.993044I
a = 2.25243 − 0.60422I
b = −1.57289 − 0.06836I
7.04961 + 4.51747I 8.24086 − 7.83910I
u = −0.456936 + 0.974335I
a = 0.404980 − 0.137063I
b = −0.206051 + 0.434618I
0.278731 + 0.366040I 1.63031 + 1.02999I
u = −0.456936 − 0.974335I
a = 0.404980 + 0.137063I
b = −0.206051 − 0.434618I
0.278731 − 0.366040I 1.63031 − 1.02999I
u = −0.662155 + 0.891568I
a = −0.504166 − 0.322965I
b = 0.445897 − 0.129011I
−0.48155 + 4.22871I 4.96713 − 5.93885I
u = −0.662155 − 0.891568I
a = −0.504166 + 0.322965I
b = 0.445897 + 0.129011I
−0.48155 − 4.22871I 4.96713 + 5.93885I
u = 0.298303 + 0.834732I
a = −2.78859 − 0.76333I
b = 1.53191 + 0.14525I
6.39960 + 1.79888I 5.99730 + 2.83305I
u = 0.298303 − 0.834732I
a = −2.78859 + 0.76333I
b = 1.53191 − 0.14525I
6.39960 − 1.79888I 5.99730 − 2.83305I
u = −0.151801 + 0.742615I
a = −0.396145 + 0.508651I
b = 0.802627 + 0.720454I
−1.41056 + 2.69993I 9.52017 − 6.18932I
u = −0.151801 − 0.742615I
a = −0.396145 − 0.508651I
b = 0.802627 − 0.720454I
−1.41056 − 2.69993I 9.52017 + 6.18932I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00049 + 1.08266I
a = −1.056910 − 0.800884I
b = 1.264430 − 0.093351I
2.43732 − 5.15744I 6.97467 + 7.14862I
u = 1.00049 − 1.08266I
a = −1.056910 + 0.800884I
b = 1.264430 + 0.093351I
2.43732 + 5.15744I 6.97467 − 7.14862I
u = −0.065045 + 0.511799I
a = 0.23309 − 5.26621I
b = −0.984688 − 0.343350I
−4.96869 + 1.33549I 1.55153 − 5.45385I
u = −0.065045 − 0.511799I
a = 0.23309 + 5.26621I
b = −0.984688 + 0.343350I
−4.96869 − 1.33549I 1.55153 + 5.45385I
u = 0.68678 + 1.39506I
a = 1.35532 + 0.47861I
b = −1.281240 + 0.198078I
3.85501 − 2.73104I 9.11804 − 0.26783I
u = 0.68678 − 1.39506I
a = 1.35532 − 0.47861I
b = −1.281240 − 0.198078I
3.85501 + 2.73104I 9.11804 + 0.26783I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 16u
15
+ ··· − 10u + 1)(u
55
+ 63u
54
+ ··· − 20918u − 169)
c
2
(u
16
+ 8u
14
+ ··· − 2u + 1)(u
55
+ u
54
+ ··· + 86u − 13)
c
3
(u
16
− 9u
14
+ ··· − 2u + 1)(u
55
+ u
54
+ ··· + 22u
2
− 23)
c
4
(u
16
− 2u
15
+ ··· + 8u
2
+ 1)(u
55
+ 3u
54
+ ··· − 12u − 11)
c
5
(u
16
+ 8u
14
+ ··· + 2u + 1)(u
55
+ u
54
+ ··· + 86u − 13)
c
6
(u
16
− 2u
15
+ ··· + 6u
2
+ 1)(u
55
− 3u
54
+ ··· + 84u − 17)
c
7
, c
8
(u
16
− 9u
14
+ ··· + 2u + 1)(u
55
+ u
54
+ ··· + 22u
2
− 23)
c
9
(u
16
+ 5u
14
+ ··· − u + 1)(u
55
− u
54
+ ··· − 325045u − 237989)
c
10
(u
16
+ 2u
15
+ ··· + 6u
2
+ 1)(u
55
− 3u
54
+ ··· + 84u − 17)
c
11
(u
16
+ 10u
15
+ ··· + 12u + 1)(u
55
+ 37u
54
+ ··· − 1784u − 289)
c
12
(u
16
+ 4u
15
+ ··· − 4u + 1)(u
55
+ 11u
54
+ ··· + 89882u + 16337)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 28y
15
+ ··· + 14y + 1)
· (y
55
− 137y
54
+ ··· + 108847246y −28561)
c
2
, c
5
(y
16
+ 16y
15
+ ··· + 10y + 1)(y
55
+ 63y
54
+ ··· − 20918y −169)
c
3
, c
7
, c
8
(y
16
− 18y
15
+ ··· − 8y + 1)(y
55
− 43y
54
+ ··· + 1012y −529)
c
4
(y
16
+ 10y
15
+ ··· + 16y + 1)(y
55
+ 21y
54
+ ··· − 4740y −121)
c
6
, c
10
(y
16
+ 10y
15
+ ··· + 12y + 1)(y
55
+ 37y
54
+ ··· − 1784y −289)
c
9
(y
16
+ 10y
15
+ ··· − 3y + 1)
· (y
55
− 23y
54
+ ··· − 63034731065y −56638764121)
c
11
(y
16
+ 2y
15
+ ··· + 116y
2
+ 1)(y
55
− 27y
54
+ ··· − 78420y −83521)
c
12
(y
16
− 18y
15
+ ··· − 18y + 1)
· (y
55
− 3y
54
+ ··· + 4960988170y −266897569)
17
